Higher Mathematics for Engineers and Scientists I
Higher Mathematics for Engineers and Scientists I MATH 3350
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This 4 page Study Guide was uploaded by Ms. Ally Koelpin on Thursday October 22, 2015. The Study Guide belongs to MATH 3350 at Texas Tech University taught by Kevin Richard Long in Fall. Since its upload, it has received 129 views. For similar materials see /class/226463/math-3350-texas-tech-university in Mathematics (M) at Texas Tech University.
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Date Created: 10/22/15
Study guide for midterm 1 Math 3350 Prof Kevin Long Sections covered 0 12 14 o 21 22 23 24 26 o 36 While the test will focus primarily on topics covered in lecture anything in the sections listed might appear on the test regardless of whether it was covered in lecture Notes and calculators 0 You may bring one page of notes front and back if you like 0 NO CALCULATORS ON THE INCLASS PART OF THE TEST Figure out what you did wrong on quizzes and homeworks Understand the mistakes you made and learn from them How to use solution sets Work through solutions stepbystep making sure that you fully understand what I did in each step Don t memorize the solutions understand them Then put them aside for a day and try to do the problems cold without looking at the solutions Repeat until you get it This may take a few days so start early Math is a contact sport When watching someone solve problems it looks easier than it really is Until you can do it yourself without looking at notes you don t know it Background 0 You ve seen exponentials and logs arising frequently Be sure you know identities relating them 0 Know how to differentiate all elementary functions 0 Be able to do integrals such as fabr dr fai JW f cos az dz f sin az dz f tan az dz f 6 dz f ze dz iIE if 0 Be sure you know Taylor polynomials and the Lagrange remainder If you re rusty on any of these they could be good things to include on your page of notes Checking procedures 0 Know how to check whether a function satis es a differential equation and a set of initial conditions Vocabulary If you don t know the language you can t understand the questions Be sure you know what is meant by the following ODE explicit solution numerical solution stepsize integrating factor order of an equation implicit solution order of accuracy local error test for exactness HS RHS closed form improved Euler s method existence amp uniqueness test for exactness Euler s method global error level contour Equation forms Know how to identify an exact equation Recognize these equation forms separable equation linear equation Benioulli equation Common errors 0 Errors due to bad notation 1 E0 L Leaving out the dx or dy in an integral is not only incorrect it can lead to an error because you forget which variable you re integrating over If you use nonstandard notation such as 81M instead of then I can t follow your work Your future bosses won t be able to follow your work either Dropping parenthesis ag writing 12 5 when you meant 02 c is an easy way to mess up a calculation Don t lose track of function arguments If you ve ever confused sin 2 with sin z2 then use parenthe ses to keep the difference clear 0 Bad algebra 1 E0 Equot Operations such as square roots logarithms exponentials and trig functions do not distribute over addi tion For example logz y y logx logy Operations such as square roots logarithms exponentials and trig functions do not commute with multi plication For example sin 2x y 2 sin 1 Here s a more subtle error if you forget to add a constant of integration then remember it a few steps later you can t just add it in at a later point For example in solving i 32 by separation of variables people sometimes do 2ydy 3z2dz 1 92 I3 2 y ass2 3 y 132 C forgot constant of integration add it now 4 which is incorrect as you can verify by checking the solution The correct procedure is Zydy 3z2dz 5 y2 x3 C add constant of integration 6 y I3 of lt7 8 Why is the rst calculation wrong Example of text annotation in Mathematica Math 3350 Fall 2008 Prof Kevin Long To annotate a Mathematica session with text click on the line where you want to type That opens up a new quotcellquot To be able to type text in it hit Alt7 Other alt keys set up other text styles such as titles and section headers as shown below Alt1 makes a big header Alt2 looks like this Alt3 looks like this Alt4 puts a line above the header I Alt5 makes a bullet entry I Alt6 makes a smaller bullet entry Alt7 makes ordinary text To enter math within a text cell do ctrl to begin math entry and ctrl to go back to text That s the control key and shift8 simultaneously to begin control and shift9 simultaneously to end To make the annotation look really good see the Mathematica Documentation Center for instructions about how to write formulas like this one fx l l x2 e 1C fx dx There are keyboard commands for entering special characters such as G and 7r or alternatively you can bring up the Math Input Palette which will let you select math symbols from a toolbar You can interleave text like this and calculations like the next cell If you don t use any Alt when writing into a cell the contents are regarded as a mathematical expression fx Sinx Exp x e xsinoc Text can go between calculations as well TextSampenb Integratef x x 1 E 2 cosx sinx
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